In a data acquisition system, the amplitude of unknown signal is adjusted via analog channel of a digital 3D oscilloscope before being sampled, quantified and coded by an analog-to-digital converter (ADC), from which binary data of certain bits in relation to signal amplitude are outputted. Such binary data is referred to as the sampling value of input signal.
Extracting information such as amplitude, frequency, etc. of the input signal directly from a series of binary data turns out to be rather difficult. Therefore, a simpler and more direct method is needed. In general data acquisition system, sampling values are converted into more visualized image and displayed on the screen by utilizing data processing components such as FPGA, DSP, etc. with the application of certain rules. Nowadays, screens are mainly of liquid crystal display (LCD), from which users can observe information carried by the signal directly.
At present, all data acquisition systems represented by digital oscilloscope are capable of adjusting brightness of waveform displayed on LCD continuously so as to achieve display effects that can satisfy different requirement. In the data processing and displaying mechanisms of digital storage oscilloscope (DSO), only two-dimensional information, i.e. amplitude and time of input signal is provided, without information of the third dimension (relationship of amplitude change over time). So there are only two kinds of status of “color available” and “color not available” in waveform display on LCD, without the information of “color and color depth”. For reasons as given above, during adjusting brightness of displayed waveform of DSO, the entire waveform turns brighter and dimmer according to a certain proportion. Under such circumstances, adjusting brightness of waveform does not make much sense.
The third generation oscilloscopes represented by digital phosphor oscilloscopes (DPO) made by Tektronix Inc. are defined as digital three-dimensional oscilloscope (DTO) in General Code for Digital Storage Oscilloscope (GB/T 15289-2009). The third generation oscilloscopes are quite different from DSO in the mechanisms of data processing and displaying.
Through multiple mapping of waveform sampling value obtained by high-speed sampling of ADC, data processing system of digital 3D oscilloscope accumulates multiple waveforms into one image that contains 3D information, i.e. amplitude, time and relationship of changes of amplitude over time, of the input signals before delivering it to LCD for display. What is displaying on LCD is an image that contains probability information of the waveform. That is to say, deeper color and lighter color will be presented at places of the image where probability of occurrence of waveform is higher and lower, respectively. Based on displaying principle of LCD, depth of waveform color will be a one-to-one correspondence to corresponding brightness of the display. Therefore, there is practical meaning to realize continuous waveform brightness adjusting in DTO. For instance, when observing some abnormal waveforms possibly exist among periodic signals with continuous recurrence, due to the fact that probability of recurrence of abnormal waveforms is much lower than that of continuous recurrence of periodic signals, it is impossible to observe abnormal waveforms of very light color under some levels of display brightness. It is therefore necessary for the users to increase brightness of displayed waveform with a certain proportion under the precondition that brightness gradation of the waveform displayed on the screen is kept unchanged, for the purpose of not only maintaining the brightness contrast of waveform probability display, but for the convenience of users in their observation and analysis of waveform of low probabilities so as to derive fault information and to take timely correction measures as well.
In order to display statistic data of waveform on LCD with a display brightness that is in line with the current brightness gradation, statistic data are generally amplified or minified in a certain proportion so as to be converted into corresponding values of three primary colors (RGB) of LCD. Assuming that the waveform occurrence is N(T,A) at the time of T and amplitude of A, and waveform brightness value corresponding to a certain type of color finally displayed on LCD is D(T,A), and proportion value corresponding to the current brightness gradation L is pL, then, the relationship among them is as the follows:D(T,A)=pL·N(T,A)  (1)
In processing system of digital 3D oscilloscope, calculation of formula (1) can be accomplished in a digital signal processor (DSP) or in a field programmable gate array (FPGA). Since computing speed of a DSP is far slower than that of a FPGA, calculation of formula (1) is generally chosen to be performed in a FPGA.
In formula (1), the proportion value pL corresponds to the current brightness gradation L. Brightness gradation is generally indicated with percentage (1%□100%) in data acquisition system. If brightness gradations are M in a digital 3D oscilloscope system, the brightness gradation L(0≦L≦M−1) will correspond to one of M proportion values. Decimal will occur unavoidably in proportion value pL, and it is generally difficult to achieve multiplication of decimal in a FPGA. If calculation of decimal is processed with calculation mode of fractional number, then:
                              p          L                =                              n            L                                m            L                                              (        2        )            
In formula (2), nL, mL are integers and are relatively prime, thus:
                              D          ⁡                      (                          T              ,              A                        )                          =                                            p              L                        ·                          N              ⁡                              (                                  T                  ,                  A                                )                                              =                                                    n                L                                            m                L                                      ·                          N              ⁡                              (                                  T                  ,                  A                                )                                                                        (        3        )            
In calculation process of formula (3), multiplication and division of integers will occur. Because computing speed of division is much slower than that of multiplication in a FPGA, speed of the entire data processing process is thus reduced. In addition, great number of built-in multiplying units of a FPGA is required to finish multiplication calculation in formula (3) respectively since there are multiple signal channels in a digital 3D oscilloscope system, and processing process of waveform display of each channel is almost fully independent of each other. Due to limited resources of built-in multiplying units in a common FPGA, such requirement may not be able to be satisfied.